initial occupation and transition likelihoods

markov.py

@@ -1,22 +1,10 @@
 from dataclasses import dataclass, field
 from typing import List
 import numpy as np
+from numpy import log as ln
 
 from maths import gaussian
 
-@dataclass
-class Likelihood:
-    forward: float  # forward likelihood
-    backward: float  # backward likelihood
-
-@dataclass
-class TimeStep:
-    states: List[Likelihood] = field(default_factory=list)
-
-@dataclass
-class Transition:
-    pass
-
 class MarkovModel:
 
     def __init__(self, states: list, observations: list = list(), state_transitions: list = list()):
@@ -27,7 +15,12 @@ class MarkovModel:
         # self.timesteps = list()
 
         self.forward = np.zeros((len(states), len(observations)))
+        self.p_obs_forward = 0
+
         self.backward = np.zeros((len(states), len(observations)))
+        self.p_obs_backward = 0
+
+        self.occupation = np.zeros((len(states), len(observations)))
 
     def get_other_state_index(self, state_in):
         """For when state changes, get other index for retrieving state transitions (FOR 0 INDEXING)"""
@@ -42,43 +35,54 @@ class MarkovModel:
         """For when state changes, get other number for retrieving state transitions (FOR 1 INDEXING)"""
         return self.get_other_state_index(state_in - 1) + 1
 
+    def populate(self):
+        self.populate_forward()
+        self.calculate_p_obs_forward()
+        self.populate_backward()
+        self.calculate_p_obs_backward()
+        self.populate_occupation()
+    
     def populate_forward(self):
         for t, observation in enumerate(self.observations): # iterate through observations (time)
             for state_index, state in enumerate(self.states):
 
                 state_number = state_index + 1 # for easier reading (arrays 0-indexed, numbers start at 1)
 
-                if t == 0: # calcualte initial
+                if t == 0: # calcualte initial, 0 = first row = initial
                     self.forward[state_index, t] = self.state_transitions[0, state_number] * gaussian(observation, state.mean, state.std_dev)
                 else:
-                    # each state for each time has two paths leading to
+                    # each state for each time has two paths leading to it, the same state (this) and the other state (other)
 
                     other_index = self.get_other_state_index(state_index)
                     other_number = other_index + 1 # for 1 indexing
                     
-                    #                      previous value             prob of changing from previous state to current
+                    # previous value * prob of changing from previous state to current
                     this_to_this = self.forward[state_index, t - 1] * self.state_transitions[state_number, state_number]
                     other_to_this = self.forward[other_index, t - 1] * self.state_transitions[other_number, state_number]
 
                     self.forward[state_index, t] = (this_to_this + other_to_this) * gaussian(observation, state.mean, state.std_dev)
 
     @property
-    def p_observations_forward(self):
+    def observation_likelihood(self):
+        """abstraction for getting p(obs|model) for future calculations (occupation/transition)"""
+        return self.p_obs_forward
+
+    def calculate_p_obs_forward(self):
 
         sum = 0
         for state_index, final_likelihood in enumerate(self.forward[:, -1]):            
             sum += final_likelihood * self.state_transitions[state_index + 1, -1] # get exit prob from state transitions
 
+        self.p_obs_forward = sum
         return sum
 
-    #TODO finish
     def populate_backward(self):
 
         # initialise from exit probabilities
         self.backward[:, -1] = self.state_transitions[1:len(self.states) + 1, -1]
 
         for t, observation in list(enumerate(self.observations[1:]))[::-1]: # iterate backwards through observations (time)
-            print(t, observation)
+            # print(t, observation)
             for state_index, state in enumerate(self.states):
 
                 state_number = state_index + 1 # for easier reading (arrays 0-indexed, numbers start at 1)
@@ -86,18 +90,70 @@ class MarkovModel:
                 other_index = self.get_other_state_index(state_index)
                 other_number = other_index + 1 # for 1 indexing
 
-                #                      previous value             prob of changing from previous state to current
+                # observation for transitions from the same state
-                this_to_this = self.backward[state_index, t + 1] * self.state_transitions[state_number, state_number]
+                this_state_gaussian = gaussian(observation, self.states[state_index].mean, self.states[state_index].std_dev)
-                other_to_this = self.backward[other_index, t + 1] * self.state_transitions[other_number, state_number]
+                # observation for transitions from the other state
+                other_state_gaussian = gaussian(observation, self.states[other_index].mean, self.states[other_index].std_dev)
                 
-                self.backward[state_index, t] = (this_to_this + other_to_this) * gaussian(observation, state.mean, state.std_dev)
+                # beta * a * b
+                this_from_this = self.backward[state_index, t + 1] * self.state_transitions[state_number, state_number] * this_state_gaussian
+                other_from_this = self.backward[other_index, t + 1] * self.state_transitions[other_number, state_number] * other_state_gaussian
 
-    #TODO finish
+                self.backward[state_index, t] = (this_from_this + other_from_this)
-    @property
+
-    def p_observations_backward(self):
+    def calculate_p_obs_backward(self):
 
         sum = 0
         for state_index, initial_likelihood in enumerate(self.backward[:, 0]):
+            # pi * b * beta
             sum += self.state_transitions[0, state_index + 1] * gaussian(self.observations[0], self.states[state_index].mean, self.states[state_index].std_dev) * initial_likelihood
 
+        self.p_obs_backward = sum
         return sum
+
+    def populate_occupation(self):
+        for t, observation in enumerate(self.observations): # iterate through observations (time)
+            for state_index, state in enumerate(self.states):
+                
+                forward_backward = self.forward[state_index, t] * self.backward[state_index, t]
+                self.occupation[state_index, t] = forward_backward / self.observation_likelihood
+
+    def transition_likelihood(self, from_index, to_index, t):
+        if t == 0:
+            print("no transition likelihood for t == 0")
+
+        forward = self.forward[from_index, t - 1]
+        transition = self.state_transitions[from_index + 1, to_index + 1]
+        emission = gaussian(self.observations[t], self.states[to_index].mean, self.states[to_index].std_dev)
+        backward = self.backward[to_index, t]
+
+        return (forward * transition * emission * backward) / self.observation_likelihood
+
+    def baum_welch_state_transitions(self):
+
+        new_transitions = np.zeros((len(self.states), len(self.states)))
+
+        # i
+        for from_index, from_state in enumerate(self.states):
+            # j
+            for to_index, to_state in enumerate(self.states):
+                
+                transition_sum = 0
+                for t in range(1, len(self.observations)):
+                    transition_sum += self.transition_likelihood(from_index, to_index, t)
+
+                occupation_sum = 0
+                for t in range(0, len(self.observations)):
+                    occupation_sum = self.occupation[to_index, t]
+
+                new_transitions[from_index, to_index] = transition_sum / occupation_sum
+
+        return new_transitions
+
+
+
+# child object to replace normal prob/likeli operations with log prob operations (normal prob for debugging)
+class LogMarkovModel(MarkovModel):
+
+    def log_state_transitions(self):
+        self.state_transitions = ln(self.state_transitions)

report/report.lyx

@@ -323,6 +323,17 @@ lstparams "language=Python,breaklines=true,frame=tb,otherkeywords={self},emph={S
 \end_inset
 
 
+\end_layout
+
+\begin_layout Standard
+\begin_inset CommandInset include
+LatexCommand lstinputlisting
+filename "../maths.py"
+lstparams "language=Python,breaklines=true,frame=tb,otherkeywords={self},emph={State},emphstyle={\\ttb\\color{darkred}},basicstyle={\\ttfamily},commentstyle={\\color{commentgreen}\\itshape},keywordstyle={\\color{darkblue}},emphstyle={\\color{red}},stringstyle={\\color{red}},caption={Maths utility file with definitions for a gaussian},label={maths-listing}"
+
+\end_inset
+
+
 \end_layout
 
 \begin_layout Standard